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1 ## Copyright (C) 1998 Auburn University. All rights reserved. |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}] =} quaternion (w) |
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22 ## @deftypefnx {Function File} {[@var{vv}, @var{theta}] =} quaternion (w) |
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23 ## @deftypefnx {Function File} {@var{w} =} quaternion (@var{a}, @var{b}, @var{c}, @var{d}) |
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24 ## @deftypefnx {Function File} {@var{w} =} quaternion (@var{vv}, @var{theta}) |
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25 ## Construct or extract a quaternion |
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26 ## |
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27 ## @example |
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28 ## w = a*i + b*j + c*k + d |
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29 ## @end example |
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30 ## |
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31 ## @noindent |
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32 ## from given data. |
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33 ## @end deftypefn |
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34 |
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35 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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36 ## Adapted-By: jwe |
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37 |
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38 function [a, b, c, d] = quaternion (w, x, y, z) |
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39 |
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40 switch (nargin) |
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41 case(1) |
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42 if (! (is_vector (w) && length (w) == 4)) |
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43 error ("input vector must be of length 4)"); |
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44 endif |
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45 ## extract data |
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46 switch (nargout) |
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47 case(4) |
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48 a = w(1); |
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49 b = w(2); |
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50 c = w(3); |
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51 d = w(4); |
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52 |
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53 case(2) |
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54 if (abs (norm (w) - 1) > 1e-12) |
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55 warning ("quaternion: ||w||=%e, setting=1 for vv, theta", norm(w)); |
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56 w = w/norm(w); |
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57 endif |
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58 [a, b, c, d] = quaternion (w); |
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59 theta = acos (d) * 2; |
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60 if (abs (theta) > pi) |
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61 theta = theta - sign (theta) * pi; |
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62 endif |
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63 sin_th_2 = norm ([a, b, c]); |
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64 |
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65 if (sin_th_2 != 0) |
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66 vv = [a, b, c] / sin_th_2; |
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67 else |
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68 vv = [a, b, c]; |
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69 endif |
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70 a = vv; |
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71 b = theta; |
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72 otherwise |
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73 usage ("[a, b, c, d] = quaternion (w) or [vv, theta] = quaternion (w)"); |
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74 endswitch |
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75 |
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76 case(2) |
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77 if (nargout != 1) |
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78 usage ("w = quaterion (vv, theta)"); |
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79 endif |
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80 vv = w; |
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81 theta = x; |
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82 |
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83 if (! is_vector (vv) || length (vv) != 3) |
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84 error ("vv must be a length three vector"); |
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85 elseif (! is_scalar (theta)) |
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86 error ("theta must be a scalar"); |
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87 elseif (norm (vv) == 0) |
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88 error ("quaternion: vv is zero"); |
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89 elseif (abs (norm (vv) - 1) > 1e-12) |
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90 warning ("quaternion: ||vv|| != 1, normalizing") |
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91 vv = vv / norm (vv); |
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92 endif |
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93 |
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94 if (abs (theta) > 2*pi) |
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95 warning ("quaternion: |theta| > 2 pi, normalizing") |
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96 theta = rem (theta, 2*pi); |
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97 endif |
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98 vv = vv * sin (theta / 2); |
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99 d = cos (theta / 2); |
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100 a = quaternion (vv(1), vv(2), vv(3), d); |
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101 |
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102 case(4) |
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103 if (nargout != 1) |
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104 usage ("w = quaterion (a, b, c, d)"); |
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105 endif |
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106 if (! (is_scalar (w) && is_scalar (x) && is_scalar (y) && is_scalar (z))) |
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107 error ("input values must be scalars"); |
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108 endif |
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109 a = [w, x, y, z]; |
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110 |
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111 otherwise |
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112 usage ("[a, b, c, d] = quaternion (w) or a = quaternion (w, x, y, z)"); |
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113 |
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114 endswitch |
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115 |
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116 endfunction |
